Question: Solve for $x$ and $y$ using elimination. ${4x-3y = 2}$ ${5x-5y = -5}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $4$ ${-20x+15y = -10}$ $20x-20y = -20$ Add the top and bottom equations together. $-5y = -30$ $\dfrac{-5y}{{-5}} = \dfrac{-30}{{-5}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {4x-3y = 2}\thinspace$ to find $x$ ${4x - 3}{(6)}{= 2}$ $4x-18 = 2$ $4x-18{+18} = 2{+18}$ $4x = 20$ $\dfrac{4x}{{4}} = \dfrac{20}{{4}}$ ${x = 5}$ You can also plug ${y = 6}$ into $\thinspace {5x-5y = -5}\thinspace$ and get the same answer for $x$ : ${5x - 5}{(6)}{= -5}$ ${x = 5}$